I actually prefer the App Store approach because that way the majority of my updates are in one place and can be done automatically in the background. The problem is that it used to work fine and they managed to break it.
I usually keep at least one prior release of Xcode on my machine, up to the latest patch for its series. So right now I have 11.5 and 11.4.1. I've hit so many problems with new versions in the past. I wish I could just let MAS handle it for me, but it's just never been an option, aside from the issues it has actually working.